Analysis of experimental data on doublet neutron-deuteron scattering at energies below the deuteron-breakup threshold on the basis of the pole approximation of the effective-range function

Abstract

On the basis of the Bargmann representation of the S matrix, the pole approximation is obtained for the effective-range function k cot δ. This approximation is optimal for describing the neutron-deuteron system in the doublet spin state. The values of r0 = 412.469 fm and v2 = −35 495.62 fm3 for the doublet low-energy parameters of neutron-deuteron scattering and the value of D = 172.678 fm2 for the respective pole parameter are deduced by using experimental results for the triton binding energy ET, the doublet neutron-deuteron scattering length a2, and van Oers-Seagrave phase shifts at energies below the deuteron-breakup threshold. With these parameters, the pole approximation of the effective-range function provides a highly precise description (the relative error does not exceed 1%) of the doublet phase shift for neutron-deuteron scattering at energies below the deuteron-breakup threshold. Physical properties of the triton in the ground (T) and virtual (v) states are calculated. The results are Bv = 0.608 MeV for the virtuallevel position and CT2 = 2.866 and Cv2 = 0.0586 for the dimensionless asymptotic normalization constants. It is shown that, in the Whiting-Fuda approximation, the values of physical quantities characterizing the triton virtual state are determined to a high precision by one parameter, the doublet neutron-deuteron scattering length a2. The effective triton radii in the ground (ρT = 1.711 fm) and virtual (ρv = 74.184 fm) states are calculated for the first time.